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Block #2,756,979

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2018, 4:41:37 AM Β· Difficulty 11.6656 Β· 4,051,090 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
f06914a1ad1e78effef04ab41e0f3515cd54bd7cf5e5ffff72e6f8a72f6aea81
View on Chainz β†—

Height

#2,756,979

Difficulty

11.665555

Transactions

2

Size

723 B

Version

2

Bits

0baa61ca

Nonce

117,658,838

Timestamp

7/20/2018, 4:41:37 AM

Confirmations

4,051,090

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

f407f24ec8f62902c30fcf0c4fa98df4fcc6566e93fe90d2f143e94bbe4ba149
Transactions (2)
Coinbase0a2ec4f48d67ff…95d11c8a7cddd6
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
bbdb07e6e3b73b…cc2e1706d4d6bb
3 in β†’ 2 out3000.2192 XPM521 B
AVa5dYbR…j5uZYCvtAKcZDzEs…8kotFYkq
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.425 Γ— 10⁹⁸(99-digit number)
84253569518322483575…03989982438834995199
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
8.425 Γ— 10⁹⁸(99-digit number)
84253569518322483575…03989982438834995199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.425 Γ— 10⁹⁸(99-digit number)
84253569518322483575…03989982438834995201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.685 Γ— 10⁹⁹(100-digit number)
16850713903664496715…07979964877669990399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.685 Γ— 10⁹⁹(100-digit number)
16850713903664496715…07979964877669990401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.370 Γ— 10⁹⁹(100-digit number)
33701427807328993430…15959929755339980799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.370 Γ— 10⁹⁹(100-digit number)
33701427807328993430…15959929755339980801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.740 Γ— 10⁹⁹(100-digit number)
67402855614657986860…31919859510679961599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.740 Γ— 10⁹⁹(100-digit number)
67402855614657986860…31919859510679961601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.348 Γ— 10¹⁰⁰(101-digit number)
13480571122931597372…63839719021359923199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.348 Γ— 10¹⁰⁰(101-digit number)
13480571122931597372…63839719021359923201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.696 Γ— 10¹⁰⁰(101-digit number)
26961142245863194744…27679438042719846399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,708,598 XPMΒ·at block #6,808,068 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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