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Block #157,470

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2013, 3:50:30 PM Β· Difficulty 9.8692 Β· 6,652,027 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f74d1f0363ffbceb613a028e47c447267ea4f6598b65ec86e88b3785ec1e663e
View on Chainz β†—

Height

#157,470

Difficulty

9.869176

Transactions

1

Size

201 B

Version

2

Bits

09de824e

Nonce

125,864

Timestamp

9/9/2013, 3:50:30 PM

Confirmations

6,652,027

Mined by

⛏️ P2SHAW7csDjrkyTy6fADU41S7MnvGqWLLrBTmA

Merkle Root

399684d33d4517c13071f6b2149d46e1f06f3bc35538a7099ae9ac825c8ee5cb
Transactions (1)
Coinbase399684d33d4517…e9ac825c8ee5cb
1 in β†’ 1 out10.2500 XPM109 B
AW7csDjr…WLLrBTmA
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.

7.013 Γ— 10⁹⁸(99-digit number)
70138724004445665489…55183710804659180799
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
7.013 Γ— 10⁹⁸(99-digit number)
70138724004445665489…55183710804659180799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.013 Γ— 10⁹⁸(99-digit number)
70138724004445665489…55183710804659180801
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
1.402 Γ— 10⁹⁹(100-digit number)
14027744800889133097…10367421609318361599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.402 Γ— 10⁹⁹(100-digit number)
14027744800889133097…10367421609318361601
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
2.805 Γ— 10⁹⁹(100-digit number)
28055489601778266195…20734843218636723199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.805 Γ— 10⁹⁹(100-digit number)
28055489601778266195…20734843218636723201
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
5.611 Γ— 10⁹⁹(100-digit number)
56110979203556532391…41469686437273446399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.611 Γ— 10⁹⁹(100-digit number)
56110979203556532391…41469686437273446401
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
1.122 Γ— 10¹⁰⁰(101-digit number)
11222195840711306478…82939372874546892799
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:57,720,049 XPMΒ·at block #6,809,496 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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