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Block #76,115

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 9:44:26 PM Β· Difficulty 9.0711 Β· 6,727,787 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
136dc44ecd9ee6a423d39a513c71369e12984a1b064926671760bb020aaad7fa
View on Chainz β†—

Height

#76,115

Difficulty

9.071140

Transactions

1

Size

200 B

Version

2

Bits

09123643

Nonce

4

Timestamp

7/21/2013, 9:44:26 PM

Confirmations

6,727,787

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

2b8b7fa8368369df33000f24d1366fde29bc4d1f4ee9f81b49be071f81459216
Transactions (1)
Coinbase2b8b7fa8368369…be071f81459216
1 in β†’ 1 out12.1400 XPM110 B
ANey87HK…MGUx5bYr
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.

9.494 Γ— 10⁹⁴(95-digit number)
94947294489314495229…69495944024466193079
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
9.494 Γ— 10⁹⁴(95-digit number)
94947294489314495229…69495944024466193079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.494 Γ— 10⁹⁴(95-digit number)
94947294489314495229…69495944024466193081
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
1.898 Γ— 10⁹⁡(96-digit number)
18989458897862899045…38991888048932386159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.898 Γ— 10⁹⁡(96-digit number)
18989458897862899045…38991888048932386161
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
3.797 Γ— 10⁹⁡(96-digit number)
37978917795725798091…77983776097864772319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.797 Γ— 10⁹⁡(96-digit number)
37978917795725798091…77983776097864772321
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
7.595 Γ— 10⁹⁡(96-digit number)
75957835591451596183…55967552195729544639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.595 Γ— 10⁹⁡(96-digit number)
75957835591451596183…55967552195729544641
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
1.519 Γ— 10⁹⁢(97-digit number)
15191567118290319236…11935104391459089279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,675,262 XPMΒ·at block #6,803,901 Β· updates every 60s
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