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Block #203,346

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/10/2013, 7:09:24 PM Β· Difficulty 9.8972 Β· 6,603,535 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
177dd5c265d3da86da67cd3b13e5c7b2c806247dfa46544d672fbbc02894fb38
View on Chainz β†—

Height

#203,346

Difficulty

9.897150

Transactions

2

Size

2.69 KB

Version

2

Bits

09e5aba1

Nonce

154,105

Timestamp

10/10/2013, 7:09:24 PM

Confirmations

6,603,535

Mined by

⛏️ P2SHAWP61hEiaZm3DZc3hxZMaedUsm1dnDFsZW

Merkle Root

36b340484f8397b4b2b67c283f6fa51ea8f1ae1000961444b91af8012eed9ca4
Transactions (2)
Coinbase0610243328c279…e54239e9e6042b
1 in β†’ 1 out10.2200 XPM109 B
AWP61hEi…1dnDFsZW
ba620db4a6449b…ab6f68f90249f2
22 in β†’ 1 out225.8800 XPM2.49 KB
AbxSykSg…BX71twYi
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.

2.106 Γ— 10⁹⁴(95-digit number)
21065330397309720189…88236884804646870649
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
2.106 Γ— 10⁹⁴(95-digit number)
21065330397309720189…88236884804646870649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.106 Γ— 10⁹⁴(95-digit number)
21065330397309720189…88236884804646870651
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
4.213 Γ— 10⁹⁴(95-digit number)
42130660794619440378…76473769609293741299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.213 Γ— 10⁹⁴(95-digit number)
42130660794619440378…76473769609293741301
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
8.426 Γ— 10⁹⁴(95-digit number)
84261321589238880756…52947539218587482599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.426 Γ— 10⁹⁴(95-digit number)
84261321589238880756…52947539218587482601
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
1.685 Γ— 10⁹⁡(96-digit number)
16852264317847776151…05895078437174965199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.685 Γ— 10⁹⁡(96-digit number)
16852264317847776151…05895078437174965201
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
3.370 Γ— 10⁹⁡(96-digit number)
33704528635695552302…11790156874349930399
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:57,699,157 XPMΒ·at block #6,806,880 Β· updates every 60s
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