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Block #23,549

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/12/2013, 8:23:23 PM Β· Difficulty 7.9603 Β· 6,772,590 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49648fafc83c9d51bf5b233fdf2adfe5c1c10d1ec2a746bab4ea17662e0a2b0d
View on Chainz β†—

Height

#23,549

Difficulty

7.960315

Transactions

1

Size

195 B

Version

2

Bits

07f5d737

Nonce

368

Timestamp

7/12/2013, 8:23:23 PM

Confirmations

6,772,590

Mined by

⛏️ P2SHAHwE4GaRP24GSSStBrfjwqSShUTA2XZSEj

Merkle Root

ca7601933dd8fd92d0ce3c76eca482ab1d59bff4022eaf2f41d902df7ae0f508
Transactions (1)
Coinbaseca7601933dd8fd…d902df7ae0f508
1 in β†’ 1 out15.7600 XPM108 B
AHwE4GaR…TA2XZSEj
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.

4.313 Γ— 10⁸⁢(87-digit number)
43138472485387133892…23769282827936122879
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
4.313 Γ— 10⁸⁢(87-digit number)
43138472485387133892…23769282827936122879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.313 Γ— 10⁸⁢(87-digit number)
43138472485387133892…23769282827936122881
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
8.627 Γ— 10⁸⁢(87-digit number)
86276944970774267785…47538565655872245759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.627 Γ— 10⁸⁢(87-digit number)
86276944970774267785…47538565655872245761
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
1.725 Γ— 10⁸⁷(88-digit number)
17255388994154853557…95077131311744491519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.725 Γ— 10⁸⁷(88-digit number)
17255388994154853557…95077131311744491521
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
3.451 Γ— 10⁸⁷(88-digit number)
34510777988309707114…90154262623488983039
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:57,613,109 XPMΒ·at block #6,796,138 Β· updates every 60s
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