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Block #506,925

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/23/2014, 9:36:01 AM Β· Difficulty 10.8157 Β· 6,305,818 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a17dd057916de1ae51b4c61e0218ebb9b37c49ccd2bc6779db6a0ac827775ca
View on Chainz β†—

Height

#506,925

Difficulty

10.815657

Transactions

1

Size

202 B

Version

2

Bits

0ad0ceee

Nonce

17,602

Timestamp

4/23/2014, 9:36:01 AM

Confirmations

6,305,818

Mined by

⛏️ P2SHAZ2SQ3G3tNTevpsyrReh5xBn3Cs4AP8u3E

Merkle Root

dc380a10b065b25ae94d4ab6e9947ea4353b2c75e8a5fa09a6012b400c299590
Transactions (1)
Coinbasedc380a10b065b2…012b400c299590
1 in β†’ 1 out8.5400 XPM111 B
AZ2SQ3G3…s4AP8u3E
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.

3.670 Γ— 10⁹⁢(97-digit number)
36705485921877914066…48559504965465194199
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
3.670 Γ— 10⁹⁢(97-digit number)
36705485921877914066…48559504965465194199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.670 Γ— 10⁹⁢(97-digit number)
36705485921877914066…48559504965465194201
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
7.341 Γ— 10⁹⁢(97-digit number)
73410971843755828132…97119009930930388399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.341 Γ— 10⁹⁢(97-digit number)
73410971843755828132…97119009930930388401
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
1.468 Γ— 10⁹⁷(98-digit number)
14682194368751165626…94238019861860776799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.468 Γ— 10⁹⁷(98-digit number)
14682194368751165626…94238019861860776801
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
2.936 Γ— 10⁹⁷(98-digit number)
29364388737502331252…88476039723721553599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.936 Γ— 10⁹⁷(98-digit number)
29364388737502331252…88476039723721553601
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
5.872 Γ— 10⁹⁷(98-digit number)
58728777475004662505…76952079447443107199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.872 Γ— 10⁹⁷(98-digit number)
58728777475004662505…76952079447443107201
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:57,745,987 XPMΒ·at block #6,812,742 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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