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Block #2,765,961

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2018, 10:03:53 AM Β· Difficulty 11.6671 Β· 4,041,119 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f3bafcb9d915f3dfa97b694ec6265625f3cc97212c56cb46d74c177d5c30b45e
View on Chainz β†—

Height

#2,765,961

Difficulty

11.667137

Transactions

2

Size

424 B

Version

2

Bits

0baac983

Nonce

846,070,601

Timestamp

7/26/2018, 10:03:53 AM

Confirmations

4,041,119

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

a2a4bb41af0b6a11123584c609494430c953040d9b33a696ee2d33603110e7e6
Transactions (2)
Coinbase8a86024af9975a…19d5806a6dc75e
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
042820a2d9f135…45bc03f3bf7711
1 in β†’ 2 out5299.9949 XPM225 B
AURDP5bd…mfdP92YCAPuqERsk…jFT5YtxU
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.

2.755 Γ— 10⁹³(94-digit number)
27555665351272919551…44395530160316225279
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
2.755 Γ— 10⁹³(94-digit number)
27555665351272919551…44395530160316225279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.755 Γ— 10⁹³(94-digit number)
27555665351272919551…44395530160316225281
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
5.511 Γ— 10⁹³(94-digit number)
55111330702545839103…88791060320632450559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.511 Γ— 10⁹³(94-digit number)
55111330702545839103…88791060320632450561
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
1.102 Γ— 10⁹⁴(95-digit number)
11022266140509167820…77582120641264901119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.102 Γ— 10⁹⁴(95-digit number)
11022266140509167820…77582120641264901121
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
2.204 Γ— 10⁹⁴(95-digit number)
22044532281018335641…55164241282529802239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.204 Γ— 10⁹⁴(95-digit number)
22044532281018335641…55164241282529802241
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
4.408 Γ— 10⁹⁴(95-digit number)
44089064562036671282…10328482565059604479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.408 Γ— 10⁹⁴(95-digit number)
44089064562036671282…10328482565059604481
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
8.817 Γ— 10⁹⁴(95-digit number)
88178129124073342565…20656965130119208959
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:57,700,736 XPMΒ·at block #6,807,079 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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