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Block #1,534,635

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 9:19:29 AM Β· Difficulty 10.6169 Β· 5,277,677 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a0261e874894773e85f69df91219c8a08717e5e19f12735d002b6291932c76c3
View on Chainz β†—

Height

#1,534,635

Difficulty

10.616935

Transactions

2

Size

7.60 KB

Version

2

Bits

0a9def7c

Nonce

29,942,814

Timestamp

4/10/2016, 9:19:29 AM

Confirmations

5,277,677

Mined by

⛏️ P2SHAYtEamXaCYQWZBo9rPHbhjDsVosvim8AJX

Merkle Root

1f9c324a1afc26bc05d3042b9bfed350a70db4b957227b40f8b0ded86dde1107
Transactions (2)
Coinbase6bca8d103b4eb3…5c85b4ca0dbead
1 in β†’ 1 out8.9400 XPM109 B
AYtEamXa…svim8AJX
3ccfea890ed612…66a730a042f53a
51 in β†’ 1 out1304.5096 XPM7.41 KB
AQhze74R…ma5pMPmn
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.

1.170 Γ— 10⁹⁴(95-digit number)
11704693819056843343…45613467847395536919
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
1.170 Γ— 10⁹⁴(95-digit number)
11704693819056843343…45613467847395536919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.170 Γ— 10⁹⁴(95-digit number)
11704693819056843343…45613467847395536921
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
2.340 Γ— 10⁹⁴(95-digit number)
23409387638113686687…91226935694791073839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.340 Γ— 10⁹⁴(95-digit number)
23409387638113686687…91226935694791073841
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
4.681 Γ— 10⁹⁴(95-digit number)
46818775276227373374…82453871389582147679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.681 Γ— 10⁹⁴(95-digit number)
46818775276227373374…82453871389582147681
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
9.363 Γ— 10⁹⁴(95-digit number)
93637550552454746749…64907742779164295359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.363 Γ— 10⁹⁴(95-digit number)
93637550552454746749…64907742779164295361
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
1.872 Γ— 10⁹⁡(96-digit number)
18727510110490949349…29815485558328590719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.872 Γ— 10⁹⁡(96-digit number)
18727510110490949349…29815485558328590721
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:57,742,511 XPMΒ·at block #6,812,311 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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