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Block #136,677

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2013, 8:32:14 AM Β· Difficulty 9.8180 Β· 6,688,790 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aede6b7091947fa94f3ab66473f6c6ad1efd6cfb8253cacf10e4b0d332a0fdf4
View on Chainz β†—

Height

#136,677

Difficulty

9.818031

Transactions

1

Size

199 B

Version

2

Bits

09d16a83

Nonce

190,486

Timestamp

8/27/2013, 8:32:14 AM

Confirmations

6,688,790

Mined by

⛏️ P2SHAY88KHSTJpyaPqTYGEt3LWdPpt88L8yacq

Merkle Root

6d058f1bf64baf3fc3d8ae3d86139e0a9966441774490cb9a5391ac5e8270ee2
Transactions (1)
Coinbase6d058f1bf64baf…391ac5e8270ee2
1 in β†’ 1 out10.3600 XPM109 B
AY88KHST…88L8yacq
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.

4.883 Γ— 10⁹⁴(95-digit number)
48835956604575597524…42914183600051364159
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
4.883 Γ— 10⁹⁴(95-digit number)
48835956604575597524…42914183600051364159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.883 Γ— 10⁹⁴(95-digit number)
48835956604575597524…42914183600051364161
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
9.767 Γ— 10⁹⁴(95-digit number)
97671913209151195048…85828367200102728319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.767 Γ— 10⁹⁴(95-digit number)
97671913209151195048…85828367200102728321
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
1.953 Γ— 10⁹⁡(96-digit number)
19534382641830239009…71656734400205456639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.953 Γ— 10⁹⁡(96-digit number)
19534382641830239009…71656734400205456641
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
3.906 Γ— 10⁹⁡(96-digit number)
39068765283660478019…43313468800410913279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.906 Γ— 10⁹⁡(96-digit number)
39068765283660478019…43313468800410913281
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
7.813 Γ— 10⁹⁡(96-digit number)
78137530567320956039…86626937600821826559
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:57,847,828 XPMΒ·at block #6,825,466 Β· updates every 60s
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