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Block #24,408

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/12/2013, 10:57:28 PM Β· Difficulty 7.9655 Β· 6,785,445 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bec93f34f65087c59d542652d3d9b4a380ecd2860c0a9b9ca2270e7c49030f52
View on Chainz β†—

Height

#24,408

Difficulty

7.965521

Transactions

1

Size

197 B

Version

2

Bits

07f72c62

Nonce

181

Timestamp

7/12/2013, 10:57:28 PM

Confirmations

6,785,445

Mined by

⛏️ P2SHAPo8xUCVJsGwZ9WcRBPobYUu9e5V3BzxL6

Merkle Root

46a3c17d8020aac60d7bc817cffa14167fed60e840dec712a78329f5e257d1dc
Transactions (1)
Coinbase46a3c17d8020aa…8329f5e257d1dc
1 in β†’ 1 out15.7400 XPM108 B
APo8xUCV…5V3BzxL6
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.

2.817 Γ— 10⁹¹(92-digit number)
28179647147814043554…39532484641818287469
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
2.817 Γ— 10⁹¹(92-digit number)
28179647147814043554…39532484641818287469
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.817 Γ— 10⁹¹(92-digit number)
28179647147814043554…39532484641818287471
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
5.635 Γ— 10⁹¹(92-digit number)
56359294295628087109…79064969283636574939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.635 Γ— 10⁹¹(92-digit number)
56359294295628087109…79064969283636574941
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
1.127 Γ— 10⁹²(93-digit number)
11271858859125617421…58129938567273149879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.127 Γ— 10⁹²(93-digit number)
11271858859125617421…58129938567273149881
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
2.254 Γ— 10⁹²(93-digit number)
22543717718251234843…16259877134546299759
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:57,722,911 XPMΒ·at block #6,809,852 Β· updates every 60s
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