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Block #143,364

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2013, 2:35:54 PM Β· Difficulty 9.8375 Β· 6,661,434 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4af627ef8badda0b38da43ae9337a389a9a914c6d7a0c0821d227fabb2103cb1
View on Chainz β†—

Height

#143,364

Difficulty

9.837493

Transactions

2

Size

426 B

Version

2

Bits

09d665f6

Nonce

75,616

Timestamp

8/31/2013, 2:35:54 PM

Confirmations

6,661,434

Mined by

⛏️ P2SHAP9mkN5CvZv9yJumdWwandb1esCp9EUL1P

Merkle Root

7d84fc077585e419aaa06429e7009baf9880b553e0f4d5a551d4ea07d9f434d3
Transactions (2)
Coinbase949a73470dcc55…e34f80d438706f
1 in β†’ 1 out10.3300 XPM109 B
AP9mkN5C…Cp9EUL1P
59d9611e10ba52…27be1cb111bdcc
1 in β†’ 2 out40.4092 XPM227 B
ANh8t6tw…Cr99fBUwAbMtYVbT…5Xxe171L
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.

7.726 Γ— 10⁹⁴(95-digit number)
77261588997575941270…40824204372412546879
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
7.726 Γ— 10⁹⁴(95-digit number)
77261588997575941270…40824204372412546879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.726 Γ— 10⁹⁴(95-digit number)
77261588997575941270…40824204372412546881
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
1.545 Γ— 10⁹⁡(96-digit number)
15452317799515188254…81648408744825093759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.545 Γ— 10⁹⁡(96-digit number)
15452317799515188254…81648408744825093761
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
3.090 Γ— 10⁹⁡(96-digit number)
30904635599030376508…63296817489650187519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.090 Γ— 10⁹⁡(96-digit number)
30904635599030376508…63296817489650187521
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
6.180 Γ— 10⁹⁡(96-digit number)
61809271198060753016…26593634979300375039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.180 Γ— 10⁹⁡(96-digit number)
61809271198060753016…26593634979300375041
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
1.236 Γ— 10⁹⁢(97-digit number)
12361854239612150603…53187269958600750079
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:57,682,451 XPMΒ·at block #6,804,797 Β· updates every 60s
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