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Block #137,156

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2013, 3:43:20 PM Β· Difficulty 9.8197 Β· 6,657,718 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f3d091baaaab340405917d776f2f6e3de641ebd6dd6c3c90712988426c8c4c3b
View on Chainz β†—

Height

#137,156

Difficulty

9.819739

Transactions

1

Size

197 B

Version

2

Bits

09d1da68

Nonce

1,499

Timestamp

8/27/2013, 3:43:20 PM

Confirmations

6,657,718

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

7a5206fb9d2785b6c6be598cf13820309b10be90f008de1224d68c8078faad51
Transactions (1)
Coinbase7a5206fb9d2785…d68c8078faad51
1 in β†’ 1 out10.3600 XPM109 B
AL2EWWZm…CwsD5iKb
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.

1.587 Γ— 10⁸⁹(90-digit number)
15875476700346902024…31623369769091092559
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
1.587 Γ— 10⁸⁹(90-digit number)
15875476700346902024…31623369769091092559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.587 Γ— 10⁸⁹(90-digit number)
15875476700346902024…31623369769091092561
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
3.175 Γ— 10⁸⁹(90-digit number)
31750953400693804049…63246739538182185119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.175 Γ— 10⁸⁹(90-digit number)
31750953400693804049…63246739538182185121
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
6.350 Γ— 10⁸⁹(90-digit number)
63501906801387608098…26493479076364370239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.350 Γ— 10⁸⁹(90-digit number)
63501906801387608098…26493479076364370241
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
1.270 Γ— 10⁹⁰(91-digit number)
12700381360277521619…52986958152728740479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.270 Γ— 10⁹⁰(91-digit number)
12700381360277521619…52986958152728740481
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
2.540 Γ— 10⁹⁰(91-digit number)
25400762720555043239…05973916305457480959
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:57,603,025 XPMΒ·at block #6,794,873 Β· updates every 60s
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