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Block #503,220

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/20/2014, 11:10:31 PM Β· Difficulty 10.8078 Β· 6,297,179 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d7cd0147caaa91b1f11e15514ba2bdfbb638cd99ec1f237ad1f7f341d12158b4
View on Chainz β†—

Height

#503,220

Difficulty

10.807800

Transactions

2

Size

1.40 KB

Version

2

Bits

0acecc02

Nonce

339,242,039

Timestamp

4/20/2014, 11:10:31 PM

Confirmations

6,297,179

Mined by

⛏️ P2SHAH828ye4SZwWhshC4cynGyDUygnAUzfGsm

Merkle Root

89553b01d894b84796cb652d3081a6b78ca9d43840e60590566b94abea558f75
Transactions (2)
Coinbasec28cdc9d37c3c3…5bd50e33b7bd84
1 in β†’ 1 out8.5700 XPM111 B
AH828ye4…nAUzfGsm
9eed6fdc901c3f…cc8a1bdf44b69f
8 in β†’ 1 out8.7977 XPM1.20 KB
AeUh4Qt2…f7iFHArP
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.

8.887 Γ— 10⁹⁷(98-digit number)
88875159062845389545…01639866261951170559
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
8.887 Γ— 10⁹⁷(98-digit number)
88875159062845389545…01639866261951170559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.887 Γ— 10⁹⁷(98-digit number)
88875159062845389545…01639866261951170561
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
1.777 Γ— 10⁹⁸(99-digit number)
17775031812569077909…03279732523902341119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.777 Γ— 10⁹⁸(99-digit number)
17775031812569077909…03279732523902341121
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
3.555 Γ— 10⁹⁸(99-digit number)
35550063625138155818…06559465047804682239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.555 Γ— 10⁹⁸(99-digit number)
35550063625138155818…06559465047804682241
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
7.110 Γ— 10⁹⁸(99-digit number)
71100127250276311636…13118930095609364479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.110 Γ— 10⁹⁸(99-digit number)
71100127250276311636…13118930095609364481
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
1.422 Γ— 10⁹⁹(100-digit number)
14220025450055262327…26237860191218728959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.422 Γ— 10⁹⁹(100-digit number)
14220025450055262327…26237860191218728961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,647,254 XPMΒ·at block #6,800,398 Β· updates every 60s
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