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Block #252,674

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/9/2013, 5:19:35 PM Β· Difficulty 9.9713 Β· 6,543,086 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cba30ae4020088b73ee9f7bb695d93dac16b923b974c57f1b0d63df612cda9e3
View on Chainz β†—

Height

#252,674

Difficulty

9.971324

Transactions

1

Size

228 B

Version

2

Bits

09f8a8ab

Nonce

5,953

Timestamp

11/9/2013, 5:19:35 PM

Confirmations

6,543,086

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

8057151ef78d3b0417907d584db204715faac6848f3f4a450ba8d98d3c9f6173
Transactions (1)
Coinbase8057151ef78d3b…a8d98d3c9f6173
1 in β†’ 2 out10.0400 XPM137 B
ARmAMwyu…P7Kn74ZTASNt3cJa…L5zCqAYM
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.

6.745 Γ— 10⁹⁢(97-digit number)
67459264373967921774…20201515420896222719
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
6.745 Γ— 10⁹⁢(97-digit number)
67459264373967921774…20201515420896222719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.745 Γ— 10⁹⁢(97-digit number)
67459264373967921774…20201515420896222721
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
1.349 Γ— 10⁹⁷(98-digit number)
13491852874793584354…40403030841792445439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.349 Γ— 10⁹⁷(98-digit number)
13491852874793584354…40403030841792445441
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
2.698 Γ— 10⁹⁷(98-digit number)
26983705749587168709…80806061683584890879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.698 Γ— 10⁹⁷(98-digit number)
26983705749587168709…80806061683584890881
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
5.396 Γ— 10⁹⁷(98-digit number)
53967411499174337419…61612123367169781759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.396 Γ— 10⁹⁷(98-digit number)
53967411499174337419…61612123367169781761
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
1.079 Γ— 10⁹⁸(99-digit number)
10793482299834867483…23224246734339563519
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:57,610,161 XPMΒ·at block #6,795,759 Β· updates every 60s
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