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Block #29,244

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 2:52:39 PM Β· Difficulty 7.9841 Β· 6,780,049 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a696ebb63ab6d7d4390ae03d905d64072e416f38377e23ba039b4d12d79f5b89
View on Chainz β†—

Height

#29,244

Difficulty

7.984138

Transactions

1

Size

197 B

Version

2

Bits

07fbf078

Nonce

39

Timestamp

7/13/2013, 2:52:39 PM

Confirmations

6,780,049

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

dfc32f74583619eb6bb6ef44166c70956a3f634f78729411ec889046b35fd79c
Transactions (1)
Coinbasedfc32f74583619…889046b35fd79c
1 in β†’ 1 out15.6700 XPM108 B
AGemJXng…w1K3MEut
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.

2.589 Γ— 10⁹³(94-digit number)
25893966060212857142…99563989276153667519
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
2.589 Γ— 10⁹³(94-digit number)
25893966060212857142…99563989276153667519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.589 Γ— 10⁹³(94-digit number)
25893966060212857142…99563989276153667521
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
5.178 Γ— 10⁹³(94-digit number)
51787932120425714285…99127978552307335039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.178 Γ— 10⁹³(94-digit number)
51787932120425714285…99127978552307335041
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
1.035 Γ— 10⁹⁴(95-digit number)
10357586424085142857…98255957104614670079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.035 Γ— 10⁹⁴(95-digit number)
10357586424085142857…98255957104614670081
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
2.071 Γ— 10⁹⁴(95-digit number)
20715172848170285714…96511914209229340159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.071 Γ— 10⁹⁴(95-digit number)
20715172848170285714…96511914209229340161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,718,414 XPMΒ·at block #6,809,292 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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