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Block #553,533

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/20/2014, 5:33:47 AM Β· Difficulty 10.9629 Β· 6,251,759 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1f7314b42621b4f3aa817104cd29946ac340d3b62c2b4ea4b9e97d20f7373ec
View on Chainz β†—

Height

#553,533

Difficulty

10.962938

Transactions

1

Size

244 B

Version

2

Bits

0af68313

Nonce

92,428,525

Timestamp

5/20/2014, 5:33:47 AM

Confirmations

6,251,759

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

ab0d712b43e7653bd3c591bf7e2fa547fee26cb8bf125d21143fc9bd93a026aa
Transactions (1)
Coinbaseab0d712b43e765…3fc9bd93a026aa
1 in β†’ 2 out8.3100 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
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.

6.798 Γ— 10⁹⁹(100-digit number)
67986443854472058073…66260440410652183039
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
6.798 Γ— 10⁹⁹(100-digit number)
67986443854472058073…66260440410652183039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.798 Γ— 10⁹⁹(100-digit number)
67986443854472058073…66260440410652183041
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
1.359 Γ— 10¹⁰⁰(101-digit number)
13597288770894411614…32520880821304366079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.359 Γ— 10¹⁰⁰(101-digit number)
13597288770894411614…32520880821304366081
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
2.719 Γ— 10¹⁰⁰(101-digit number)
27194577541788823229…65041761642608732159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.719 Γ— 10¹⁰⁰(101-digit number)
27194577541788823229…65041761642608732161
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
5.438 Γ— 10¹⁰⁰(101-digit number)
54389155083577646458…30083523285217464319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.438 Γ— 10¹⁰⁰(101-digit number)
54389155083577646458…30083523285217464321
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
1.087 Γ— 10¹⁰¹(102-digit number)
10877831016715529291…60167046570434928639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.087 Γ— 10¹⁰¹(102-digit number)
10877831016715529291…60167046570434928641
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
2.175 Γ— 10¹⁰¹(102-digit number)
21755662033431058583…20334093140869857279
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:57,686,410 XPMΒ·at block #6,805,291 Β· updates every 60s
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