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Block #2,761,946

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2018, 6:23:39 PM Β· Difficulty 11.6541 Β· 4,069,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f22577165968e4f87d3c0aeddd04f56c52d7a5066798949c08df3bc5f4d03a47
View on Chainz β†—

Height

#2,761,946

Difficulty

11.654088

Transactions

2

Size

1018 B

Version

2

Bits

0ba77257

Nonce

944,509,015

Timestamp

7/23/2018, 6:23:39 PM

Confirmations

4,069,193

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

3f0089fd0327854a4b2c052f11b37fcca6eef3dc974b8418d5a325018c2fb245
Transactions (2)
Coinbasec4e588155fbf65…7522d91daa392d
1 in β†’ 1 out7.3700 XPM110 B
AZtxQr2F…7grUWrUz
d8fabf8edc70f6…4688c889a863d4
5 in β†’ 2 out10.1794 XPM818 B
AUMCKnnY…qdp4oBWjAbdFAmqz…8tzbHoBV
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.

2.806 Γ— 10⁹⁡(96-digit number)
28062913616618568575…59393503918642626559
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
2.806 Γ— 10⁹⁡(96-digit number)
28062913616618568575…59393503918642626559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.806 Γ— 10⁹⁡(96-digit number)
28062913616618568575…59393503918642626561
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
5.612 Γ— 10⁹⁡(96-digit number)
56125827233237137151…18787007837285253119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.612 Γ— 10⁹⁡(96-digit number)
56125827233237137151…18787007837285253121
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
1.122 Γ— 10⁹⁢(97-digit number)
11225165446647427430…37574015674570506239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.122 Γ— 10⁹⁢(97-digit number)
11225165446647427430…37574015674570506241
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
2.245 Γ— 10⁹⁢(97-digit number)
22450330893294854860…75148031349141012479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.245 Γ— 10⁹⁢(97-digit number)
22450330893294854860…75148031349141012481
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
4.490 Γ— 10⁹⁢(97-digit number)
44900661786589709721…50296062698282024959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.490 Γ— 10⁹⁢(97-digit number)
44900661786589709721…50296062698282024961
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
8.980 Γ— 10⁹⁢(97-digit number)
89801323573179419442…00592125396564049919
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:57,893,259 XPMΒ·at block #6,831,138 Β· updates every 60s
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