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Block #4,457

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/9/2013, 12:34:24 PM Β· Difficulty 7.3192 Β· 6,792,163 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bad5a321a85b05f5eb20bdb9cda0491f61b185b14ee30d8459f6e1388d01f7c1
View on Chainz β†—

Height

#4,457

Difficulty

7.319154

Transactions

1

Size

202 B

Version

2

Bits

0751b415

Nonce

489

Timestamp

7/9/2013, 12:34:24 PM

Confirmations

6,792,163

Mined by

⛏️ P2SHAPJmvq7wkcaCu9mGfekMymG8vsUtbNwEJA

Merkle Root

e283d1c14f89a65722e5ac5c9c5cbb3a6d01d5b46ed0f4f6d300802f5ea8ac1d
Transactions (1)
Coinbasee283d1c14f89a6…00802f5ea8ac1d
1 in β†’ 1 out18.6400 XPM108 B
APJmvq7w…UtbNwEJA
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.

2.751 Γ— 10¹⁰⁡(106-digit number)
27517117624784277596…98683335365928395059
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
2.751 Γ— 10¹⁰⁡(106-digit number)
27517117624784277596…98683335365928395059
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.751 Γ— 10¹⁰⁡(106-digit number)
27517117624784277596…98683335365928395061
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
5.503 Γ— 10¹⁰⁡(106-digit number)
55034235249568555193…97366670731856790119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.503 Γ— 10¹⁰⁡(106-digit number)
55034235249568555193…97366670731856790121
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
1.100 Γ— 10¹⁰⁢(107-digit number)
11006847049913711038…94733341463713580239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.100 Γ— 10¹⁰⁢(107-digit number)
11006847049913711038…94733341463713580241
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
2.201 Γ— 10¹⁰⁢(107-digit number)
22013694099827422077…89466682927427160479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,616,958 XPMΒ·at block #6,796,619 Β· updates every 60s
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