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Block #267,843

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/21/2013, 2:54:36 PM Β· Difficulty 9.9584 Β· 6,535,785 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3aed28687665bc5632ff14032696cd79367448c4b0f25016dab42f96349d7d4e
View on Chainz β†—

Height

#267,843

Difficulty

9.958445

Transactions

1

Size

199 B

Version

2

Bits

09f55ca5

Nonce

167,645

Timestamp

11/21/2013, 2:54:36 PM

Confirmations

6,535,785

Mined by

⛏️ P2SHAXHqpR716k7HAKyiRQyC63yPtEEXddpMfV

Merkle Root

2dac5d05e64477cbcf8332c569236f290e00d11cd549b1ad899e92ba48b9a978
Transactions (1)
Coinbase2dac5d05e64477…9e92ba48b9a978
1 in β†’ 1 out10.0700 XPM109 B
AXHqpR71…EXddpMfV
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.

1.354 Γ— 10⁹⁡(96-digit number)
13547424552782659577…94993515350185172799
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
1.354 Γ— 10⁹⁡(96-digit number)
13547424552782659577…94993515350185172799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.354 Γ— 10⁹⁡(96-digit number)
13547424552782659577…94993515350185172801
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
2.709 Γ— 10⁹⁡(96-digit number)
27094849105565319155…89987030700370345599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.709 Γ— 10⁹⁡(96-digit number)
27094849105565319155…89987030700370345601
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
5.418 Γ— 10⁹⁡(96-digit number)
54189698211130638310…79974061400740691199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.418 Γ— 10⁹⁡(96-digit number)
54189698211130638310…79974061400740691201
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
1.083 Γ— 10⁹⁢(97-digit number)
10837939642226127662…59948122801481382399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.083 Γ— 10⁹⁢(97-digit number)
10837939642226127662…59948122801481382401
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
2.167 Γ— 10⁹⁢(97-digit number)
21675879284452255324…19896245602962764799
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:57,673,056 XPMΒ·at block #6,803,627 Β· updates every 60s
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