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Block #202,423

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/10/2013, 5:24:02 AM Β· Difficulty 9.8950 Β· 6,614,556 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ce6f9f8b492b4b9bdb7bc8b0b01167a7ab1b9a6b1ef011ae262f739079a5113d
View on Chainz β†—

Height

#202,423

Difficulty

9.895001

Transactions

1

Size

199 B

Version

2

Bits

09e51ec5

Nonce

78,603

Timestamp

10/10/2013, 5:24:02 AM

Confirmations

6,614,556

Mined by

⛏️ P2SHAP52EE3FezHothJTJo3Xw2Hi1LZhqfNP3e

Merkle Root

2f34f7b0a67fc6792e02e929f3d1630965b66a5e2a59b73f646244b6684c13a7
Transactions (1)
Coinbase2f34f7b0a67fc6…6244b6684c13a7
1 in β†’ 1 out10.2000 XPM109 B
AP52EE3F…ZhqfNP3e
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.

2.459 Γ— 10⁹⁴(95-digit number)
24596791942876646935…66962491374573820239
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
2.459 Γ— 10⁹⁴(95-digit number)
24596791942876646935…66962491374573820239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.459 Γ— 10⁹⁴(95-digit number)
24596791942876646935…66962491374573820241
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
4.919 Γ— 10⁹⁴(95-digit number)
49193583885753293870…33924982749147640479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.919 Γ— 10⁹⁴(95-digit number)
49193583885753293870…33924982749147640481
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
9.838 Γ— 10⁹⁴(95-digit number)
98387167771506587741…67849965498295280959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.838 Γ— 10⁹⁴(95-digit number)
98387167771506587741…67849965498295280961
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
1.967 Γ— 10⁹⁡(96-digit number)
19677433554301317548…35699930996590561919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.967 Γ— 10⁹⁡(96-digit number)
19677433554301317548…35699930996590561921
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
3.935 Γ— 10⁹⁡(96-digit number)
39354867108602635096…71399861993181123839
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:57,779,870 XPMΒ·at block #6,816,978 Β· updates every 60s
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