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Block #516,745

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2014, 12:53:29 PM Β· Difficulty 10.8488 Β· 6,279,329 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8f67754be0167444c76be0a62355a2dab091d269d13de7511c0fb0dc4d93e7b8
View on Chainz β†—

Height

#516,745

Difficulty

10.848752

Transactions

1

Size

208 B

Version

2

Bits

0ad947cd

Nonce

49,454,747

Timestamp

4/29/2014, 12:53:29 PM

Confirmations

6,279,329

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

31ea1b06a98e950b70bf895906029c065cefe7b37a8a518003b0fb4fdcec6535
Transactions (1)
Coinbase31ea1b06a98e95…b0fb4fdcec6535
1 in β†’ 1 out8.4800 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.

3.367 Γ— 10⁹⁹(100-digit number)
33673998919468189739…27360826847310053119
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
3.367 Γ— 10⁹⁹(100-digit number)
33673998919468189739…27360826847310053119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.367 Γ— 10⁹⁹(100-digit number)
33673998919468189739…27360826847310053121
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
6.734 Γ— 10⁹⁹(100-digit number)
67347997838936379478…54721653694620106239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.734 Γ— 10⁹⁹(100-digit number)
67347997838936379478…54721653694620106241
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
1.346 Γ— 10¹⁰⁰(101-digit number)
13469599567787275895…09443307389240212479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.346 Γ— 10¹⁰⁰(101-digit number)
13469599567787275895…09443307389240212481
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
2.693 Γ— 10¹⁰⁰(101-digit number)
26939199135574551791…18886614778480424959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.693 Γ— 10¹⁰⁰(101-digit number)
26939199135574551791…18886614778480424961
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
5.387 Γ— 10¹⁰⁰(101-digit number)
53878398271149103583…37773229556960849919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.387 Γ— 10¹⁰⁰(101-digit number)
53878398271149103583…37773229556960849921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.077 Γ— 10¹⁰¹(102-digit number)
10775679654229820716…75546459113921699839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,612,688 XPMΒ·at block #6,796,073 Β· updates every 60s
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