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Block #207,756

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2013, 3:09:30 PM Β· Difficulty 9.9040 Β· 6,602,543 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f0ad1c601efec9f8e37a112fba8d9bed15071299fe0f512ad123b1f6dc77877
View on Chainz β†—

Height

#207,756

Difficulty

9.903963

Transactions

1

Size

199 B

Version

2

Bits

09e76a22

Nonce

127,731

Timestamp

10/13/2013, 3:09:30 PM

Confirmations

6,602,543

Mined by

⛏️ P2SHANcX13Fk7xSX8wFr5zRphRpXHx1biNXNGx

Merkle Root

8c40f2d0a7a53dc924f20356e314ca3cd0ac5066ec5301b3af07ed365db21f6e
Transactions (1)
Coinbase8c40f2d0a7a53d…07ed365db21f6e
1 in β†’ 1 out10.1800 XPM109 B
ANcX13Fk…1biNXNGx
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.

3.202 Γ— 10⁹⁴(95-digit number)
32025884682362622961…28746677521373363199
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
3.202 Γ— 10⁹⁴(95-digit number)
32025884682362622961…28746677521373363199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.202 Γ— 10⁹⁴(95-digit number)
32025884682362622961…28746677521373363201
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
6.405 Γ— 10⁹⁴(95-digit number)
64051769364725245923…57493355042746726399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.405 Γ— 10⁹⁴(95-digit number)
64051769364725245923…57493355042746726401
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
1.281 Γ— 10⁹⁡(96-digit number)
12810353872945049184…14986710085493452799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.281 Γ— 10⁹⁡(96-digit number)
12810353872945049184…14986710085493452801
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
2.562 Γ— 10⁹⁡(96-digit number)
25620707745890098369…29973420170986905599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.562 Γ— 10⁹⁡(96-digit number)
25620707745890098369…29973420170986905601
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
5.124 Γ— 10⁹⁡(96-digit number)
51241415491780196738…59946840341973811199
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:57,726,469 XPMΒ·at block #6,810,298 Β· updates every 60s
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