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Block #192,419

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/3/2013, 8:42:11 PM Β· Difficulty 9.8747 Β· 6,633,155 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3eca2136d5f9adf2394c9cccfcb2601b1d57e2b7a3f2c23099e91eac6759811
View on Chainz β†—

Height

#192,419

Difficulty

9.874669

Transactions

1

Size

198 B

Version

2

Bits

09dfea52

Nonce

202,446

Timestamp

10/3/2013, 8:42:11 PM

Confirmations

6,633,155

Mined by

⛏️ P2SHAcwApu3JRN74VsULk4fWdpqmWaZSSWqRw6

Merkle Root

e6992ff95477d57ad71746526f8255c319b32d97a3422fdc4d35dce10a47254e
Transactions (1)
Coinbasee6992ff95477d5…35dce10a47254e
1 in β†’ 1 out10.2400 XPM109 B
AcwApu3J…ZSSWqRw6
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.

2.456 Γ— 10⁹³(94-digit number)
24568286032851206953…45307208485527977799
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
2.456 Γ— 10⁹³(94-digit number)
24568286032851206953…45307208485527977799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.456 Γ— 10⁹³(94-digit number)
24568286032851206953…45307208485527977801
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
4.913 Γ— 10⁹³(94-digit number)
49136572065702413906…90614416971055955599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.913 Γ— 10⁹³(94-digit number)
49136572065702413906…90614416971055955601
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
9.827 Γ— 10⁹³(94-digit number)
98273144131404827812…81228833942111911199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.827 Γ— 10⁹³(94-digit number)
98273144131404827812…81228833942111911201
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
1.965 Γ— 10⁹⁴(95-digit number)
19654628826280965562…62457667884223822399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.965 Γ— 10⁹⁴(95-digit number)
19654628826280965562…62457667884223822401
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
3.930 Γ— 10⁹⁴(95-digit number)
39309257652561931124…24915335768447644799
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:57,848,692 XPMΒ·at block #6,825,573 Β· updates every 60s
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