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Block #498,862

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/18/2014, 7:51:52 AM Β· Difficulty 10.7845 Β· 6,337,950 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2ba98a9c4819d6cbb102e30505b7c56cf4b512d89fa1a4d5f45efd3390248684
View on Chainz β†—

Height

#498,862

Difficulty

10.784507

Transactions

1

Size

201 B

Version

2

Bits

0ac8d57a

Nonce

2,291

Timestamp

4/18/2014, 7:51:52 AM

Confirmations

6,337,950

Mined by

⛏️ P2SHASqdfRNpTunqNuXsxMBqCryK9KGfUbuqS8

Merkle Root

fd0f1c59019da7e9e0bac30cbc7f0e14797031427e3876e4d21c5fbbb76d08d5
Transactions (1)
Coinbasefd0f1c59019da7…1c5fbbb76d08d5
1 in β†’ 1 out8.5800 XPM109 B
ASqdfRNp…GfUbuqS8
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.

7.051 Γ— 10⁹⁸(99-digit number)
70519727625588594617…91274555358307932159
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
7.051 Γ— 10⁹⁸(99-digit number)
70519727625588594617…91274555358307932159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.051 Γ— 10⁹⁸(99-digit number)
70519727625588594617…91274555358307932161
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
1.410 Γ— 10⁹⁹(100-digit number)
14103945525117718923…82549110716615864319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.410 Γ— 10⁹⁹(100-digit number)
14103945525117718923…82549110716615864321
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
2.820 Γ— 10⁹⁹(100-digit number)
28207891050235437847…65098221433231728639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.820 Γ— 10⁹⁹(100-digit number)
28207891050235437847…65098221433231728641
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
5.641 Γ— 10⁹⁹(100-digit number)
56415782100470875694…30196442866463457279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.641 Γ— 10⁹⁹(100-digit number)
56415782100470875694…30196442866463457281
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
1.128 Γ— 10¹⁰⁰(101-digit number)
11283156420094175138…60392885732926914559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.128 Γ— 10¹⁰⁰(101-digit number)
11283156420094175138…60392885732926914561
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:57,938,780 XPMΒ·at block #6,836,811 Β· updates every 60s
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