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Block #1,534,501

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 7:08:35 AM Β· Difficulty 10.6171 Β· 5,278,393 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
edb237b92b7cc014ec472af5f4ff03eb400f45bd360b149cd56308b3c24a023f
View on Chainz β†—

Height

#1,534,501

Difficulty

10.617109

Transactions

3

Size

15.03 KB

Version

2

Bits

0a9dfae1

Nonce

1,772,066,024

Timestamp

4/10/2016, 7:08:35 AM

Confirmations

5,278,393

Mined by

⛏️ P2SHATbZqzg1veoPBZAtuYP3AFjXbDfJM3tuwv

Merkle Root

62ce229a91c334d6cd0f0b06d68f027422743c836322686a8a4357a58b4285a7
Transactions (3)
Coinbase97c87d46cef67c…9f2108ed9728ab
1 in β†’ 1 out9.0200 XPM109 B
ATbZqzg1…fJM3tuwv
03b522f3db5ef1…0a6573e420efd7
51 in β†’ 1 out570.5631 XPM7.42 KB
ARsKVXmZ…Acmbj4WZ
efe084f34e4ee5…f605c81b71a7da
51 in β†’ 1 out302.2436 XPM7.41 KB
AR7QKpEW…2simPWn7
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.

1.645 Γ— 10⁹⁢(97-digit number)
16452142593045107306…94233948153244106239
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
1.645 Γ— 10⁹⁢(97-digit number)
16452142593045107306…94233948153244106239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.645 Γ— 10⁹⁢(97-digit number)
16452142593045107306…94233948153244106241
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
3.290 Γ— 10⁹⁢(97-digit number)
32904285186090214613…88467896306488212479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.290 Γ— 10⁹⁢(97-digit number)
32904285186090214613…88467896306488212481
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
6.580 Γ— 10⁹⁢(97-digit number)
65808570372180429227…76935792612976424959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.580 Γ— 10⁹⁢(97-digit number)
65808570372180429227…76935792612976424961
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
1.316 Γ— 10⁹⁷(98-digit number)
13161714074436085845…53871585225952849919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.316 Γ— 10⁹⁷(98-digit number)
13161714074436085845…53871585225952849921
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
2.632 Γ— 10⁹⁷(98-digit number)
26323428148872171691…07743170451905699839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.632 Γ— 10⁹⁷(98-digit number)
26323428148872171691…07743170451905699841
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:57,747,183 XPMΒ·at block #6,812,893 Β· updates every 60s
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