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Block #493,358

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/15/2014, 4:03:21 PM Β· Difficulty 10.6985 Β· 6,345,576 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72b2bb5de629d619e21d9737f2739e9e1d535814cc4420b406f5e498ee2c4334
View on Chainz β†—

Height

#493,358

Difficulty

10.698485

Transactions

1

Size

207 B

Version

2

Bits

0ab2cfe2

Nonce

30,742

Timestamp

4/15/2014, 4:03:21 PM

Confirmations

6,345,576

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

215f6b82dc1ab41d56ca487f975a3d79f1d72b684154d96c2301b234204f85cc
Transactions (1)
Coinbase215f6b82dc1ab4…01b234204f85cc
1 in β†’ 1 out8.7200 XPM116 B
AbwWkWZt…kawDhufa
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.

1.999 Γ— 10⁹⁷(98-digit number)
19995824260686514334…91543791170984605649
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
1.999 Γ— 10⁹⁷(98-digit number)
19995824260686514334…91543791170984605649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.999 Γ— 10⁹⁷(98-digit number)
19995824260686514334…91543791170984605651
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
3.999 Γ— 10⁹⁷(98-digit number)
39991648521373028669…83087582341969211299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.999 Γ— 10⁹⁷(98-digit number)
39991648521373028669…83087582341969211301
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
7.998 Γ— 10⁹⁷(98-digit number)
79983297042746057338…66175164683938422599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.998 Γ— 10⁹⁷(98-digit number)
79983297042746057338…66175164683938422601
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
1.599 Γ— 10⁹⁸(99-digit number)
15996659408549211467…32350329367876845199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.599 Γ— 10⁹⁸(99-digit number)
15996659408549211467…32350329367876845201
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
3.199 Γ— 10⁹⁸(99-digit number)
31993318817098422935…64700658735753690399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.199 Γ— 10⁹⁸(99-digit number)
31993318817098422935…64700658735753690401
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:57,955,736 XPMΒ·at block #6,838,933 Β· updates every 60s
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