XPM Prime Explorer symbol
XPMPrime Explorer

Block #203,849

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/11/2013, 3:09:30 AM Β· Difficulty 9.8976 Β· 6,591,584 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8d4348928bddf47b63f2a938dec5aedb008f7a6bf44b3d1403b44e93eaf0306
View on Chainz β†—

Height

#203,849

Difficulty

9.897609

Transactions

2

Size

850 B

Version

2

Bits

09e5c9af

Nonce

1,680

Timestamp

10/11/2013, 3:09:30 AM

Confirmations

6,591,584

Mined by

⛏️ P2SHAXxeYLr9y2xRPjuWZy9gymgtbMv2Vq4SPL

Merkle Root

270c2abf383250c4e7d0e86d4e98403d1c2cb9efc2208161a0ef0919de09b6cd
Transactions (2)
Coinbase0367b9c48650a3…bbe90553d6b751
1 in β†’ 1 out10.2000 XPM109 B
AXxeYLr9…v2Vq4SPL
087c84cc6d12be…288480df7b61a2
5 in β†’ 2 out51.1200 XPM651 B
AH8MuWec…2bVG62mKARArVQTd…TbA6fDTa
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.

1.511 Γ— 10⁹⁴(95-digit number)
15110613717767533250…45192206086388841519
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
1.511 Γ— 10⁹⁴(95-digit number)
15110613717767533250…45192206086388841519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.511 Γ— 10⁹⁴(95-digit number)
15110613717767533250…45192206086388841521
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
3.022 Γ— 10⁹⁴(95-digit number)
30221227435535066501…90384412172777683039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.022 Γ— 10⁹⁴(95-digit number)
30221227435535066501…90384412172777683041
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
6.044 Γ— 10⁹⁴(95-digit number)
60442454871070133003…80768824345555366079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.044 Γ— 10⁹⁴(95-digit number)
60442454871070133003…80768824345555366081
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
1.208 Γ— 10⁹⁡(96-digit number)
12088490974214026600…61537648691110732159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.208 Γ— 10⁹⁡(96-digit number)
12088490974214026600…61537648691110732161
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
2.417 Γ— 10⁹⁡(96-digit number)
24176981948428053201…23075297382221464319
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:57,607,527 XPMΒ·at block #6,795,432 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK