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Block #185,054

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2013, 3:04:32 AM Β· Difficulty 9.8622 Β· 6,624,591 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2eaa47284c13f37cb7c9d62f382ed15a19466df647db5a76df55a6d7fba8173
View on Chainz β†—

Height

#185,054

Difficulty

9.862216

Transactions

2

Size

359 B

Version

2

Bits

09dcba34

Nonce

24,964

Timestamp

9/29/2013, 3:04:32 AM

Confirmations

6,624,591

Mined by

⛏️ P2SHANvtpRa12yh2D3uGdgT2ggcH58QjsraDJz

Merkle Root

f96cc3fa3cc56064a3be5c1f68b92b23582865cd5cfda240d8fe049aee0d02b4
Transactions (2)
Coinbase89b65579a2504a…d1a1274b6786b5
1 in β†’ 1 out10.2800 XPM110 B
ANvtpRa1…QjsraDJz
5ad3ee9d633eb1…c3cf376635ff74
1 in β†’ 1 out10.2600 XPM159 B
AN7CTbAY…CXZXPsEU
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.

6.210 Γ— 10⁹⁴(95-digit number)
62100024310307044108…95415576064288601929
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
6.210 Γ— 10⁹⁴(95-digit number)
62100024310307044108…95415576064288601929
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.210 Γ— 10⁹⁴(95-digit number)
62100024310307044108…95415576064288601931
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
1.242 Γ— 10⁹⁡(96-digit number)
12420004862061408821…90831152128577203859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.242 Γ— 10⁹⁡(96-digit number)
12420004862061408821…90831152128577203861
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
2.484 Γ— 10⁹⁡(96-digit number)
24840009724122817643…81662304257154407719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.484 Γ— 10⁹⁡(96-digit number)
24840009724122817643…81662304257154407721
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
4.968 Γ— 10⁹⁡(96-digit number)
49680019448245635286…63324608514308815439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.968 Γ— 10⁹⁡(96-digit number)
49680019448245635286…63324608514308815441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.936 Γ— 10⁹⁡(96-digit number)
99360038896491270573…26649217028617630879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,721,240 XPMΒ·at block #6,809,644 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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