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Block #29,314

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 3:07:11 PM Β· Difficulty 7.9843 Β· 6,765,981 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3eea520edb16eae2dd85a5f79e0879b144c3aa519a6774aa0045c39cd3022736
View on Chainz β†—

Height

#29,314

Difficulty

7.984312

Transactions

1

Size

197 B

Version

2

Bits

07fbfbd9

Nonce

388

Timestamp

7/13/2013, 3:07:11 PM

Confirmations

6,765,981

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

f0f285fc7d5916daf64ff8d9db162dab3b6243d581fbee5e3bf8441265a5b762
Transactions (1)
Coinbasef0f285fc7d5916…f8441265a5b762
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.

1.249 Γ— 10⁹³(94-digit number)
12497245319419727264…84305527381654532059
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
1.249 Γ— 10⁹³(94-digit number)
12497245319419727264…84305527381654532059
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.249 Γ— 10⁹³(94-digit number)
12497245319419727264…84305527381654532061
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
2.499 Γ— 10⁹³(94-digit number)
24994490638839454528…68611054763309064119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.499 Γ— 10⁹³(94-digit number)
24994490638839454528…68611054763309064121
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
4.998 Γ— 10⁹³(94-digit number)
49988981277678909057…37222109526618128239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.998 Γ— 10⁹³(94-digit number)
49988981277678909057…37222109526618128241
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
9.997 Γ— 10⁹³(94-digit number)
99977962555357818114…74444219053236256479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.997 Γ— 10⁹³(94-digit number)
99977962555357818114…74444219053236256481
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:57,606,411 XPMΒ·at block #6,795,294 Β· updates every 60s
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